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QuestionThe first side of a triangle is 8 m8 \mathrm{~m} shorter than the second side. The third side is 4 times the first side. The perimeter is 26 m26 \mathrm{~m}. Find the length of each side.

Studdy Solution

STEP 1

Assumptions1. The first side of the triangle is8m shorter than the second side. . The third side is4 times as long as the first side.
3. The perimeter of the triangle is26m.
4. The lengths of the sides are positive real numbers.

STEP 2

Let's denote the sides of the triangle as follows- First side xx m- Second side x+8x +8 m (since it's8m longer than the first side) - Third side 4x4x m (since it's4 times the first side)

STEP 3

The perimeter of a triangle is the sum of the lengths of all its sides. So we can write the equation for the perimeter as followsx+(x+8)+x=26x + (x +8) +x =26

STEP 4

implify the equation by combining like terms.
6x+8=266x +8 =26

STEP 5

Subtract8 from both sides of the equation to isolate the term with xx.
x=26−8x =26 -8

STEP 6

Calculate the right side of the equation.
6x=186x =18

STEP 7

Divide both sides of the equation by6 to solve for xx.
x=186x = \frac{18}{6}

STEP 8

Calculate the value of xx.
x=3x =3

STEP 9

Now that we have the value of xx, we can find the lengths of the sides of the triangle.
- First side x=3x =3 m- Second side x+8=3+8x +8 =3 +8 m- Third side 4x=4×34x =4 \times3 m

STEP 10

Calculate the lengths of the second and third sides.
- Second side 3+8=3 +8 = m- Third side 4×3=124 \times3 =12 mSo, the lengths of the sides of the triangle are3m,m, and12m.

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